The cars will be assembled at Toyota's plant in Georgetown, Kentucky. The facility, which employs 7,000 people, is Toyota's largest plant outside Japan. (Read: 10 most fuel-efficient cars)

This will not be the first time the Japan-based automaker has shipped cars to third countries from its U.S. factories. Toyota began exporting vehicles from the United States in 1988 and now ships about 100,000 vehicles to 19 countries from its U.S. facilities.

Toyota (TM) also exports some Avalon large sedans from the United States, as well as Sequoia SUVs and Tundra pickups.

Toyota produces 1.5 million vehicles a year in its North American factories -- a figure that includes plants in Canada and Mexico. In addition, it imports about 600,000 cars a year into the United States from Japan.

The Camry is Toyota's best-selling car in the United States. It has been the best-selling passenger car in America for 13 of the last 14 years. It was recently completely redesigned for the 2012 model year.

The U.S. government recently ratified a free trade agreement with South Korea. Plans to export Camrys to South Korea were underway prior to the agreement, Toyota spokesman Javier Moreno said.

Toyota said the strengthening Japanese currency makes it more cost effective to ship cars from Kentucky to South Korea -- across nearly 7,000 miles of land and sea -- than to export them from Japan.

"The recent appreciation of the [Japanese] yen has made it challenging for us to export vehicles from Japan," Moreno said.